WASHINGTON (Reuters) – A two-year U.S. budget deal on Tuesday cleared a Senate procedural vote that all but assured its passage by a simple majority later this week in the Democratic-controlled chamber.

The Senate voted 67-33 to limit debate on the measure, exceeding the required 60 votes and overcoming the opposition of conservative Republicans who objected to increased near-term government spending.

Twelve Republicans joined 53 Democrats and two independents in supporting the measure, which aims to minimize the threat of another government shutdown through October 1, 2015. It won passage in the House of Representatives by an overwhelming margin last week.

A 16-day partial government shutdown in October left many Republicans skittish about withholding their support for legislation to keep agencies operating.

The Senate, where Democrats have a 55-45 majority, is expected to vote on final passage of the budget measure as early as Wednesday.

Several conservative Republican senators, including Tea Party supporters Rand Paul and Ted Cruz, tried to stop the measure and keep automatic “sequester” spending cuts in place. The budget deal eases some of the sequester cuts by allowing budgets for government agencies and discretionary programs to rise by $63 billion over two years in exchange for future savings elsewhere.

But a mix of moderate and conservative Republican senators voted to proceed to an up-or-down vote on the deal, which was negotiated by Democratic Senator Patty Murray and Republican Representative Paul Ryan.

The margin of victory is expected to be close on the final vote, however. Senator Lamar Alexander, a Republican from Tennessee who faces a tough re-election primary challenge, voted “yes” on the procedural question but said he would ultimately oppose the deal.

“I will vote against the budget agreement because it avoids the federal government’s most urgent need: reducing the growth of runaway entitlement spending,” Alexander said in a statement.

The measure sets spending levels ranging from the military to national parks at just over $1 trillion for two fiscal years. Assuming it wins final passage and is signed by President Barack Obama, Congress must then pass a spending measure that allocates funds by January 15 when current government spending authority expires.